Many of the basic principles and concepts used by molecular chemists only apply to a small fraction of solid-state compounds One example of these principles is the law of definite proportions, i.e., the concept that a compound has a definite stoichiometry. Nonstoichiometric extended solids such as FeO.sub.x with 1.05&lt;.times.&lt;1.13 are common to many solid-state phase diagrams. Another example is the ability of molecular chemists to predict the structure and reactivity of an unknown compound based on a knowledge of the bonding and coordination of the atoms involved. Except for simple derivative compounds based upon simple chemical substitution, the ability to predict the structures of new solid-state compounds is practically impossible due to the large variability in coordination numbers found in extended solids. A third example is the concept of a reaction mechanism. The usefulness of knowing a particular reaction mechanism in solid-state synthesis is limited because most solid-state synthetic techniques produce thermodynamic products. Also, most solid-state synthesis techniques do not permit the course of a reaction to be followed. Hence, formation of new compounds via solid-state chemistry poses distinctive problems that cannot be addressed by principles applicable to molecular chemists.
In non-solid-state chemistry, formation of chemical compounds generally occurs via one or more reactions wherein reactants chemically combine under defined conditions to yield a desired product. Molecular chemists formulate synthesis strategies with a view toward controlling, at least in part, the applicable reaction kinetics. That is, the reaction conditions are adjusted so as to optimize the interactions of reactant atoms or molecules. To maximize the yield of product, the reactants are usually combined in stoichiometric proportions and intermixed sufficiently under optimal conditions to ensure that reactant atoms or molecules efficiently contact each other. With gases and liquids, intermixture is readily effected by agitation; even if the reactants are not deliberately agitated, diffusion and connection can be sufficient to achieve intermixture in many instances.
However, when the reactants are solids, achieving sufficient intermixture of reactant atoms and molecules can be a serious problem. Some degree of intermixture of the reactants can be achieved by comminuting them and blending the resulting particles together; but, fragmentation is neither always practical nor desirable. Also, fragmentation is incapable of effecting intermixture on a molecular or atomic scale. Intermixture of solid reactants by diffusion is extremely limited under most conditions due to excessively high activation energies associated with solid-state diffusion. Mechanical agitation of the reactants is usually impossible. Other methods are also sometimes employed, but they are usually limited to specific reaction systems.
Solid-state reactions have become important over the last several decades, particularly in view of their utility in manufacturing integrated circuits, photovoltaic cells, and in other thin-film technologies. For example, according to existing methods, a first elemental reactant such as a metal is deposited atop a second elemental reactant such as silicon, thereby forming a bulk "reaction couple." To overcome the high activation energy of diffusion and achieve at least a degree of interdiffusion of the elemental reactants within a manageable time, the temperature of the reaction couple is increased substantially, usually by annealing at many hundreds of degrees Celsius. As the reaction couple is heated past a characteristic threshold temperature, a bulk "diffusion couple" is formed wherein atoms from each reactant begin to diffuse together and form an amorphous interdiffusion zone at the interface between the elemental deposits. Increasing the temperature causes a corresponding increase in the kinetic energy of reactant atoms which correspondingly increases both their rate of interdiffusion and the rate at which the interdiffusion zone expands into the elemental deposits. As the reactant atoms interdiffuse, a concentration gradient of one reactant relative to the other reactant forms across the thickness dimension of the interdiffusion zone, as indicated in the following example: ##STR1##
Achieving interdiffusion of a bulk reaction couple by high-temperature methods as practiced in the art often results in loss of control of the outcome of the reaction, particularly if the desired outcome is an amorphous (non-crystalline) material. Almost invariably, one or more crystalline products ("phases") spontaneously forms at various levels in the concentration gradient before interdiffusion is complete. Of course, once these crystalline phases form, the previously amorphous character of the interdiffusion zone is lost.
Crystallization within the interdiffusion zone is usually triggered by "nucleation." Nucleation is generally recognized as a major impediment to forming many amorphous materials and certain crystalline alloys by solid-state chemistry. Nucleation is very difficult, if not impossible, to control by known methods.
As used herein, "nucleation" is the formation of one or more "islands" or "embryos" of at least partially ordered atoms in a sea of amorphous (unordered) atoms. Each crystal nucleus can be envisioned as an infinitesimally small (due to entropy factors) droplet of a substantially crystalline material having a definite stoichiometry. In a bulk diffusion couple, nucleation usually occurs in one or more of the possible binary amorphous regions represented at various depths in an interdiffusion zone. For example, in the Si.vertline.Fe interdiffusion zone shown hereinabove, nucleation can occur in one or more of the interdiffusion-zone regions predominated by 1Fe:2Si, 1Fe:1Si, or 3Fe:1Si. Such nucleated binary phases are usually thermodynamically more stable than the surrounding amorphous material; therefore, once nucleation starts, it often progresses to Complete crystallization of the surrounding amorphous region. Nucleation can be triggered, for example, on a minute trace of a foreign substance acting as a nucleus around which atoms can become arranged in an ordered configuration.
Nucleation, however, does not inevitably lead to formation of a crystalline phase. It is appreciated by persons skilled in the art that crystal nuclei must exceed a critical size before crystallization will progress to completion. When a crystal nucleus exceeds the critical size, its total free energy decreases with further growth (accretion) thereof, thereby favoring further accretion. When crystal nuclei are smaller than critical size, their surface energy may be too high to thermodynamically favor enlargement. Such subcritical nuclei will tend to shrink or disappear altogether. Thus, there is a certain energy barrier on the path leading from nucleation to complete crystallization.
Phase interfaces are particularly prone to crystallization. One example of a phase interface is the boundary between a first and a second solid-state reactant layer in a bulk diffusion couple. Another example is the boundary between a crystal nucleus and surrounding amorphous material. Phase interfaces are characterized by large stresses and strains which can be reduced by nucleation and accretion. Also, phase interfaces are often characterized by relatively large concentrations of impurities, relatively large concentration gradients, and enhanced diffusion rates, which can act in concert to lower the surface energy of crystal nuclei.
With bulk diffusion couples as known in the art, every thermodynamically stable binary phase in the corresponding phase diagram will nucleate to form a crystalline phase. According to current understanding, the interdiffusion zone between two diffusion-couple reactants is a phase interface that favors formation of a crystalline phase. The first thermodynamically stable crystalline phase that forms in the amorphous interdiffusion zone generates two new phase interfaces with the amorphous interdiffusion zone. As the first crystalline phase grows, the stoichiometry at the two new phase interfaces changes, ultimately favoring the formation of other thermodynamically stable crystalline phases having stoichiometries different both from one another and from the first crystalline phase that formed. The relative amounts of each crystalline phase formed in the interface zone will be determined in part by the diffusion constants of the reactant elements through each of the crystalline phases that have already formed. As a result, it is extremely difficult if not impossible by known methods to produce an alloy having a composition corresponding to a non-thermodynamically stable phase.
Hence, in a bulk diffusion couple, the various thermodynamically stable phases in the corresponding phase diagram that form are sequentially generated. However, not every compound in the phase diagram is necessarily formed. For example, with an iron-silicon diffusion couple, Fe.sub.5 Si.sub.3 does not nucleate. Also, the same sequence of phases is observed in various diffusion couples involving the same reactants, regardless of the stoichiometric composition of a specific diffusion couple.
Therefore, formation of either amorphous solidstate compounds or single crystalline compounds (to the exclusion of other crystalline compounds) by known methods involving bulk diffusion couples is either impossible or extremely difficult.
The problems associated with bulk diffusion couples are particularly difficult to overcome when attempting to synthesize ternary and higher-order alloys. Forming such amorphous compounds is virtually impossible because of the tendency of binary compounds to nucleate long before interdiffusion of three or more reactants is complete. Forming many crystalline ternary alloys is also virtually impossible because the probability of nucleating a ternary phase is inherently much lower than the probability of nucleating any of several possible binary phases. Also, the subsequent growth of ternary-phase nuclei is much more difficult since diffusion to a nucleus of atoms or molecules of each of three reactants must occur in order to enlarge the ternary nucleus. What inevitably happens is that various stable binary phases nucleate and form crystalline phases before nucleation of the desired ternary phase can begin.
Therefore, while other chemists can manipulate the starting conditions and reaction parameters to achieve kinetic control of a synthetic reaction, solid-state chemists have had to be content with the hope that the desired phase from a high-temperature diffusion couple is the thermodynamically most stable phase and thus will form to the exclusion of other possible phases. In the case of reactions involving three or more elemental reactants, the attendant lack of control of a high-temperature reaction pathway limits the possible product phases to thermodynamically stable phases, which are almost always among the intermediate binary phases, not higher-order phases.